Question

3. Classify each function according to whether it is a vertical stretch, a vertical compression, a horizontal

Answer 1

The classifications of the functions are

• A vertical stretch --- p(x) = 4f(x)
• A vertical compression --- g(x) = 0.65f(x)
• A horizontal stretch --- k(x) = f(0.5x)
• A horizontal compression  --- h(x) = f(14x)

How to classify each function accordingly?

The categories of the functions are given as

• A vertical stretch
• A vertical compression
• A horizontal stretch
• A horizontal compression

The general rules of the above definitions are:

• A vertical stretch --- g(x) = a f(x) if |a| > 1
• A vertical compression --- g(x) = a f(x) if 0 < |a| < 1
• A horizontal stretch --- g(x) = f(bx) if 0 < |b| < 1
• A horizontal compression  --- g(x) = f(bx) if |b| > 1

Using the above rules and highlights, we have the classifications of the functions to be

• A vertical stretch --- p(x) = 4f(x)
• A vertical compression --- g(x) = 0.65f(x)
• A horizontal stretch --- k(x) = f(0.5x)
• A horizontal compression  --- h(x) = f(14x)

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